Is there a list of all the people who attempted to prove the parallel postulate (also known as the fifth postulate or the Euclid axiom) in Euclidean geometry? Wikipedia has a page on the subject but the list given there is far too short.

Here is what I have collected so far, any addition is welcome.

Archimedes (~ -287- -212)
Posidonios (~-135 ~-51)
Geminus (~-10 ~60)
Claude Ptoleme (~90 ~168)
Proclus (412 485)
Simplicius (~490 ~560)
Thabit ibn Qurra (826 901)
Al-Abbās ibn Said al-Jawharī (~800 ~860)
Abu'l Abbas al-Fadl ibn Hatim Al-Nayrizi (~865 ~922)
Ibn al-Haytham (965 1039)
Avicenna (980-1037)
Omar Khayyam (1048-1131)
Nasir ad-Din at-Tusi (1201-1274)
Erazmus Ciołek Witelo (~1230-~1300)
Rabbi Levi ben Gershom (1288-1344)
Pietro Antonio Cataldi (1548-1626)
Giovanni Alfonso Borelli (1608-1679)
John Wallis (1616-1703)
Giovanni Girolamo Saccheri (1667-1733)
Johann Heinrich Lambert (1728-1777)
Joseph-Louis Lagrange (1736-1813)
Adrien-Marie Legendre (1752-1833)
Farkas Bolyai (1775-1856)
Ferdinand Carl Schweikart (1780-1859)
Friedrich Ludwig Wachter (1792-1818)
Franz Adolph Taurinus (1794-1874)
Viktor Yakovlevich Bunyakovsky (1804-1889)

EDIT: added Farkas Bolyai, Joseph-Louis Lagrange, as pointed out in the comments.

  • $\begingroup$ What is your question? $\endgroup$ – Alexandre Eremenko May 30 '18 at 15:57
  • $\begingroup$ @eremenko Is there a list of all the people who attempted to prove the parallel postulate (also known as the fifth postulate or the Euclid axiom) in Euclidean geometry? An answer would provide a reference to such a list or the list itself. $\endgroup$ – coudy May 30 '18 at 16:55
  • $\begingroup$ What do you mean exactly by “prove the parallel postulate in Euclidean geometry”? Deriving it from the other axioms of Euclid? If so, I think a number of these authors attempted no such thing. $\endgroup$ – Viktor Blasjo May 30 '18 at 20:47
  • 1
    $\begingroup$ Grabiner, Judith V., Why did Lagrange “prove” the parallel postulate?, Am. Math. Mon. 116, No. 1, 3-18 (2009). ZBL1163.01009. (Also gives you a ready “parallel postulate” search link in Zentralblatt.) $\endgroup$ – Francois Ziegler May 31 '18 at 10:33
  • 1
    $\begingroup$ János Bolyai's father, Farkas Bolyai, should be on the list. He famously wrote to his son:"Detest it as lewd intercourse, it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life... Do not try the parallels in that way: I know that way all along. I have measured that bottomless night, and all the light and all the joy of my life went out there.". Kids never listen. $\endgroup$ – Conifold May 31 '18 at 21:11

There are several nearly insurmountable problems with carrying out this project, such as where to draw the line (pun intended) in determining what suffices as "attempted to prove" and the huge number of mathematical papers, books, manuscripts, letters, etc. in over a dozen languages that would have to be analyzed. Also, simply coming up with such a list of names is certainly of little interest, as one would want to know at least something about what each person did in trying to resolve the parallel postulate issue, since such a list of names would probably include a large minority, if not an actual majority, of the mathematicians who lived before the 1800s. For example, I notice Gauss is missing from your list, but surely Gauss must have made some attempts in his early years (perhaps in the 1790s or the first decade of the 1800s) --- see here and here.

That said, if you really want to dive into this (which will likely be a several decades project), one place to begin is

Bibliography of Non-Euclidean Geometry, Including the Theory of Parallels, the Foundations of Geometry, and Space of $n$ Dimensions by D. M'L. Y. Sommerville (1911, xii + 403 pages)

Since this book was published in 1911, there is a huge amount of subsequently published historical literature that you'll also need to go through, as I am sure there are many things that have come to light since the time Sommerville published his bibliography.

| improve this answer | |
  • $\begingroup$ As far as I know, Gauss did the exact contrary to trying to prove the fifth postulate. He instead developed a geometry in which the postulate does not hold and convinced himself that it was consistent. He did not publish anything for fear of what people might say. $\endgroup$ – coudy May 30 '18 at 17:18
  • $\begingroup$ I very strongly suspect Gauss first tried to prove the parallel postulate. This might be supported by an entry in his diary, I don't know, and it might be recorded in something he later wrote (such as a letter). Or maybe not. But I find it very unlikely (to say the least) that he would have begun his investigation into the matter by seeking to disprove the existence of a proof of the parallel postulate. $\endgroup$ – Dave L Renfro May 30 '18 at 18:00
  • $\begingroup$ Let me draw the line at mathematicians for which there is at least some historical evidence that they published or wrote down a proof of the postulate. $\endgroup$ – coudy May 31 '18 at 11:31

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.